The letter "h" is NEVER pronounced in French.

For most words that begin with "h", the "h" functions in the same way as if it were not even written and the word behaves exactly the same as if it began with a vowel. Consequently, the elision process occurs: e.g. "l'homme", the vowel of "le" is deleted (elision).

For a few words that begin with an "h", the "h" remains unpronounced but elision does not occur. This "h" is called "h aspiré" (e.g. huit, huitième, le huitième jour). You cannot tell from looking at a word beginning with "h" whether it is an "h aspiré". However you can always check a dictionary where words starting with an "h aspiré" are marked by an asterisk * or some other mark.

Examples:

Cet homme s'habille pour prendre l'hélicoptère à l'hôpital.

La fantôme du héros ne hante pas la haute plaine de Hongrie.